Stress-induced wellbore failures are common in oilfield exploration and production. This problem has been an important concern for operators, as borehole collapses and lost circulation during well drilling can cause economic losses. Such stress-induced wellbore failures can also cause problems in production operations, as sanding control and management are of utmost importance for the economy of a field. Therefore, to safely drill a deep well for hydrocarbon exploration or production, it is necessary to predict the wellbore stability and avoid wellbore failures, and a better understanding of the rock mechanical properties and failure behavior is essential to improve the economics of an oilfield development.
Most of current wellbore stability models are based on the assumption that formation rock is a continuous isotropic medium, thus the traditional shear/tensile failure models of intact rockmass are used. For example, Bradley (1979) laid a milestone for inclined wellbore analysis by providing an analytical solution based on linear, isotropic elasticity.
However, in most cases anisotropy behavior of formation is found, and wellbore failures related to bedding or laminated formations have been widely recognized as a common cause of wellbore instability. Thus it is difficult to apply the theory based on the assumption that formation rock is a continuous isotropic medium on the actual analysis of laminated formations.
To approach the anisotropy behavior of formation, the mechanics of anisotropic material was introduced into engineering in early the 20th century, and much research has been carried out in the area of finding the proper Green's functions to describe the elastic displacement response of a linear elastic medium to the applied force. For example, for transversely isotropic materials, the 3-D Green's functions in a full-space have been obtained. In addition, a generalized formalism to express the deformation of dislocations and cracks in an anisotropic medium has also been obtained. Unfortunately, due to the mathematical difficulty, there is no unique analytical solution to the problem of a borehole embedded in a transversely isotropic material.
Further, several models of the deformation and failure of laminated/bedding rock around a cylindrical cavity have been developed. For example, Aadnoy treats rock as a transversely isotropic elastic material with failure been governed by a Mohr-Coulomb criterion incorporating a single plane of weakness. However, Aadnoy's model has disadvantage that it simplified the transversely isotropic model by using only three elastic parameters, rather than the five that are actually required. Willson et al. also adopted the single plane failure model in analyzing the wellbore stability problems in bedding formations, but unrealistically assumed isotropic elastic behavior when computing the deformation and induced stresses in their model.
Still another approach is to use the existing numerical methods, such as the 3-D Finite Element Method (FEM), to solve for the stress and deformation around a borehole embedded in a laminated formation, and then predict the borehole stability by appropriately incorporating the failure criterion. However, these numerical methods have not been applied to field applications systemically. There are two reasons. First, in laminated formations, boundaries or interfaces between different formations pose great difficulties in discretization of the elements, especially in the cases when the borehole axis is inclined to the axis of the laminated formation plane. Second, 3-D FEM is a computational time costly approach and it is impossible to use this method in a log-based analysis.